Principles of Oxidation-Reduction Reactions in Biology

Linking Redox Potential to Free Energy

The most critical aspect of redox reactions in biochemistry is that the transfer of electrons is coupled to the release of energy. This allows the cell to capture the "downhill" flow of electrons and use it to do work, such as synthesizing ATP.

The relationship between the change in standard reduction potential ($\Delta E_0'$) and the standard free energy change ($\Delta G^{\circ'}$) is defined by the following equation:

$\Delta G^{\circ'} = -nF\Delta E_0'$

Where:

• $n$ is the number of electrons transferred.
• $F$ is the Faraday constant.

When electrons move from a donor (low $E_0'$) to an acceptor (high $E_0'$), the $\Delta E_0'$ is positive. Because of the negative sign in the formula, this results in a negative $\Delta G^{\circ'}$, indicating an exergonic reaction where energy is released.

Worked Example: NADH to O$_2$

Let's calculate the energy released when NADH transfers its electrons to oxygen, a process central to the electron transport chain:

1. Identify the potentials:
   • The reduction of O$_2$ to H$_2$O has an $E_0'$ of $+0.82\text{ V}$.
   • The oxidation of NADH to NAD$^+$ has an $E_0'$ of $+0.32\text{ V}$ (note that for the oxidation reaction, we use the value associated with the reduction of NAD$^+$).
2. Calculate $\Delta E_0'$: $\Delta E_0' = 0.82\text{ V} + 0.32\text{ V} = 1.14\text{ V}$
3. Calculate $\Delta G^{\circ'}$: Using $n = 2$ (since NADH transfers two electrons) and the Faraday constant ($96.48\text{ kJ mol}^{-1}\text{V}^{-1}$): $\Delta G^{\circ'} = -(2) \cdot (96.48\text{ kJ mol}^{-1}\text{V}^{-1}) \cdot (1.14\text{ V})$ $\Delta G^{\circ'} = -220\text{ kJ mol}^{-1}$

This massive release of energy is what the cell harnesses to drive the formation of a proton gradient across the inner mitochondrial membrane.

Biological Application: The Proton Gradient

In the mitochondria, the "downhill" flow of electrons from NADH or FADH$_2$ to O$_2$ is not a single jump. Instead, electrons pass through a series of protein complexes in the electron transport chain (ETC). As electrons move through these complexes, the energy released is used to pump protons ($H^+$) from the mitochondrial matrix into the intermembrane space.

This creates an electrochemical potential known as a proton gradient. This gradient acts like water behind a dam; the "uphill" accumulation of protons stores potential energy that can later be released as protons flow back into the matrix, driving the synthesis of ATP.

Summary Comparison:

• NADH enters at Complex I, leading to the pumping of 10 protons.
• FADH$_2$ enters at Complex II, which does not pump protons, resulting in only 6 protons being pumped through the subsequent complexes.
• Consequently, NADH provides more energy for ATP production than FADH$_2$.

A Note on Safety: Reactive Oxygen Species (ROS)

While redox reactions are essential, they can be dangerous. If the reduction of oxygen is incomplete, it can produce highly reactive molecules called reactive oxygen species (ROS), such as superoxide ions. These can damage DNA, proteins, and membranes. Fortunately, cells employ specialized enzymes like superoxide dismutase and catalase to neutralize these threats and maintain cellular integrity.